This　work　confirms　the　performance　gain　achieved　by　deploying　a　simultaneously　transmitting　and　reflecting　reconfigurable　intelligent　surface　(STAR-RIS)　in　covert　communication.　To　maximize　the　system　covert　rate,　we　jointly　optimize　the　power　allocation　coefficients　at　the　transmitter　and　the　transmission　and　reflection　coefficients　at　the　STAR-RIS,　subject　to　the　delay-constrained　and　power-constrained.　Furthermore,　we　propose　a　two-stage　alternating　optimization　algorithm　based　on　the　semidefinite　relaxation　(SDR)　method　to　derive　the　optimal　solutions　to　the　above　non-convex　optimization　problem.　The　effectiveness　and　superiority　of　the　proposed　algorithm　and　STAR-RIS-assisted　covert　scheme　are　demonstrated　by　the　numerical　results.　　©　2023　IEEE.